854 Prof. Chalk's on the Hydro dynamical Theory of the 



effect ; and as the different circles may be assumed to produce 

 independent effects, there will be in the interior of the coil from 

 end to end impulses of equal intensity analogous to those which 

 were supposed in art. 7 to be generated in a magnet by a regular 

 gradation of atomic density. The whole action being symme- 

 trical with respect to the axis of the coil, the impulses may with 

 close approximation be assumed, for the same reasons as in the 

 case of the magnet, to be concentrated along the axis, sup- 

 posing the shape of the coil to be that of a hollow cylinder, 

 and the radii of the interior and exterior surfaces to be small. 



51. In fact, so far as regards the indirect action now under 

 consideration, the hydrodynamical circumstances due to the coil 

 are exactly analogous to those due to a magnet, the force of the 

 battery performing the part which was attributed to the grada- 

 tion of atomic density of the magnet. Consequently the mathe- 

 matical investigations contained in the Numbers of the Philoso- 

 phical Magazine for July 1869 and June 1872, and already ap- 

 plied in the theory of the magnet given in arts 6-15 of the pre- 

 sent essay, may with equal reason be applied to the problem of 

 the action of a galvanic coil, although in each case the adopted 

 solution of the hydrodynamical problem can only be considered 

 to be approximately applicable. It suffices, however, for draw- 

 ing the inference that the galvanic action of a cylindrical coil 

 approximates to the action of a cylindrical magnet, which con- 

 clusion is confirmed by well-known experiments made with 

 Ampere's solenoids. Accordingly the formulas obtained in art. 

 15 for the directive action of a large magnet on a small magnetic 

 needle will be considered to be equally applicable to the action 

 of a galvanic coil on the needle, so far, at least, as regards the 

 indirect action of the coil. 



52. But experiment has also shown that there is a decided 

 difference between the action of a magnet and that of a coil 

 under the same circumstances. This fact has been specially 

 established by the experiments of the Astronomer Royal the 

 results of which are given in the Philosophical Transactions, 

 vol. clxii. pp. 489-491. I propose to account for the difference 

 by taking into consideration the direct effect of the circular 

 motions treated of in arts. 45-47, to which there is nothing cor- 

 responding in the hydrodynamical circumstances of the streams 

 of a magnet. This explanation admits of being supported by 

 the following argument. 



Prom results obtained in art. 15 it appears that if at any point 

 P, the coordinates of which in the longitudinal and transverse 

 directions are/> and q, the directive force of a large magnet of 

 length 21 on a small one in the longitudinal direction be Z v and 

 that in the transverse direction be X„ 



